How can we define common sense in an AI agent?
I came up with a few ideas I would argue are valuable in motivating the idea of common sense for a machine learning model. 


Common sense is retrospective. We define it in terms of a past (sensible) actions and conditions, and we can say someone has good common sense on the basis of their behavior, which we can view as the sum of their historical actions and the degree to which they were sensible. 
The actions alone are not sufficient for demonstrating common sense; the mental model(s) that generated those actions is important as well. Why did the individual take those sensible actions? Is their reasoning behind their action sensible as well, or did they merely get lucky (put another way, does their generally not sensical mental model produce sensible actions in certain cases and non sensical actions in most others)? This hints that common sense is contingent on the rationalization of the actions themselves. 
Given the former, common sense is contingent on the enumeration of possible actions and choosing the right one, given the context of the situation. For example, I’m walking on a path and see a snail. What are some actions? I could keep walking, stop and admire it for a while, step on it, or eat it. The first two options are sensible if I value the snail as a living being. The first option is sensible if I’m in a rush. The second and fourth may be sensible if I’m a chef exploring nature for new potential ingredients. The third option if I recognize the snail as invasive. We say someone has common sense when, given the context, the actions chosen are sensible and we can reason about them intuitively. 


My guess is that, the intuition behind the perceived sense of an action is what you’re after. I’d argue that, ultimately, the intuition of common sense is defined by the person developing the model and will have to do with the formulation of the model (e.g it’s assumptions, the objective function, etc). After all, common sense is subjective and context specific. 

Concretely, a model can have common sense if the developer bakes it in and we can use inferential methods to demonstrate this. For example, in a Word2Vec model, we might see that $\mathsf{Paris} \mapsto \mathsf{France}$ and would expect that $\mathsf{Tokyo} \mapsto \mathsf{Japan}$. To interrogate this, we might do some vector math and find that $\mathsf{Paris} - \mathsf{France} + \mathsf{Tokyo} = \mathsf{Japan}$. How and if the AI model develops the larger association between $\mathsf{Capital} \mapsto \mathsf{Country}$, however, comes down to how the developer built and trained the model to recapitulate their own common sense.